How do I Bevel an Edge within an Edge?
I dont have enough rep points to comment, but, to comment, I did what you wanted, just with CTRL+B, not sure where the problems is with your bevel. Maybe, CTRL+A first ? scale / rotation / location....

OP edit: SpaceKat had recommended resetting my settings. Which I did by reinstalling the latest version of Blender 2.79B, the original version I used was 2.78. Using the newer version of Blender fixed the issue right away no problems at all. I wanted to give SpaceKat proper credit so I edited the post.